Blood pressure (BP) is a critical vital sign that hypertensive patients regularly measure. In this study, we propose a novel BP estimation framework to distill the knowledge from a multi-modal model to a uni-modal BP estimation model through teacher-student training. The multi-modal BP estimation model consists of three components: first, a gated recurrent unit network that generates features from photoplethysmogram, electrocardiogram, age, height, and weight; second, an attention mechanism that integrates each feature into joint embeddings; and third, a regression layer that estimates BP from the joint embeddings. The uni-modal BP estimation model has similar components to the multi-modal model but uses only PPG signal. BP is predicted by the embeddings extracted from the uni-modal model, and these embeddings are trained to be as similar as possible to the joint embeddings extracted from the multi-modal model. The proposed method demonstrates absolute prediction errors of 5.24±6.41 and 3.49±3.85 mmHg for systolic blood pressure and diastolic blood pressure in the MIMIC-III dataset, satisfying the AAMI standard.